Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
Correct Answer
$10115
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5950 × 7% × 10
= $5950 ×7/100 × 10
= 5950 × 7 × 10/100
= 41650 × 10/100
= 416500/100
= $4165
Thus, Simple Interest = $4165
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4165
= $10115
Thus, Amount to be paid = $10115 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 7% × 10)
= $5950 + ($5950 ×7/100 × 10)
= $5950 + (5950 × 7 × 10/100)
= $5950 + (41650 × 10/100)
= $5950 + (416500/100)
= $5950 + $4165 = $10115
Thus, Amount (A) to be paid = $10115 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5950, the simple interest in 1 year
= 7/100 × 5950
= 7 × 5950/100
= 41650/100 = $416.5
Thus, simple interest for 1 year = $416.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $416.5 × 10 = $4165
Thus, Simple Interest (SI) = $4165
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4165
= $10115
Thus, Amount to be paid = $10115 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(5) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(8) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(10) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.